x^2-22x+100=0

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Solution for x^2-22x+100=0 equation: 


Simplifying
x2 + -22x + 100 = 0

Reorder the terms:
100 + -22x + x2 = 0

Solving
100 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -22x + -100 + x2 = 0 + -100

Reorder the terms:
100 + -100 + -22x + x2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -22x + x2 = 0 + -100
-22x + x2 = 0 + -100

Combine like terms: 0 + -100 = -100
-22x + x2 = -100

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -100 + 121

Reorder the terms:
121 + -22x + x2 = -100 + 121

Combine like terms: -100 + 121 = 21
121 + -22x + x2 = 21

Factor a perfect square on the left side:
(x + -11)(x + -11) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -11) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -11 = 4.582575695

Simplifying
x + -11 = 4.582575695

Reorder the terms:
-11 + x = 4.582575695

Solving
-11 + x = 4.582575695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + x = 4.582575695 + 11

Combine like terms: -11 + 11 = 0
0 + x = 4.582575695 + 11
x = 4.582575695 + 11

Combine like terms: 4.582575695 + 11 = 15.582575695
x = 15.582575695

Simplifying
x = 15.582575695


Subproblem 2
x + -11 = -4.582575695

Simplifying
x + -11 = -4.582575695

Reorder the terms:
-11 + x = -4.582575695

Solving
-11 + x = -4.582575695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + x = -4.582575695 + 11

Combine like terms: -11 + 11 = 0
0 + x = -4.582575695 + 11
x = -4.582575695 + 11

Combine like terms: -4.582575695 + 11 = 6.417424305
x = 6.417424305

Simplifying
x = 6.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.582575695, 6.417424305}

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